arXiv subjects

T. Imamura

Publications and source records attributed to T. Imamura.

21 records · Page 2Linked to original sources

arXiv2004

Polynuclear growth model, GOE$^2$ and random matrix with deterministic source

We present a random matrix interpretation of the distribution functions which have appeared in the study of the one-dimensional polynuclear growth (PNG) model with external sources. It is shown that the distribution, GOE$^2$, which is defined as the square of the GOE Tracy-Widom distribution, can be obtained as the scaled largest eigenvalue distribution of a special case of a random matrix model with a deterministic source, which have been studied in a different context previously. Compared to the original interpretation of the GOE$^2$ as ``the square of GOE'', ours has an advantage that it can also describe the transition from the GUE Tracy-Widom distribution to the GOE$^2$. We further demonstrate that our random matrix interpretation can be obtained naturally by noting the similarity of the topology between a certain non-colliding Brownian motion model and the multi-layer PNG model with an external source. This provides us with a multi-matrix model interpretation of the multi-point height distributions of the PNG model with an external source.

math-ph↗

arXiv2004

Fluctuations of the one-dimensional polynuclear growth model with external sources

The one-dimensional polynuclear growth model with external sources at edges is studied. The height fluctuation at the origin is known to be given by either the Gaussian, the GUE Tracy-Widom distribution, or certain distributions called GOE$^2$ and $F_0$, depending on the strength of the sources. We generalize these results and show that the scaling limit of the multi-point equal time height fluctuations of the model are described by the Fredholm determinant, of which the limiting kernel is explicitly obtained. In particular we obtain two new kernels, describing transitions between the above one-point distributions. One expresses the transition from the GOE$^2$ to the GUE Tracy-Widom distribution or to the Gaussian; the other the transition from $F_0$ to the Gaussian. The results specialized to the fluctuation at the origin are shown to be equivalent to the previously obtained ones via the Riemann-Hilbert method.

math-ph↗

arXiv2003

Fluctuations of a one-dimensional polynuclear growth model in a half space

We consider the multi-point equal time height fluctuations of a one-dimensional polynuclear growth model in a half space. For special values of the nucleation rate at the origin, the multi-layer version of the model is reduced to a determinantal process, for which the asymptotics can be analyzed. In the scaling limit, the fluctuations near the origin are shown to be equivalent to those of the largest eigenvalue of the orthogonal/symplectic to unitary transition ensemble at soft edge in random matrix theory.

cond-mat.stat-mech↗